I put Hayir beste ders baslamayacak (sorry no Turkish keyboard) and it was marked as incorrect. Am I right in thinking that I have moved the emphasis from "not starting at FIVE" to the CLASS not starting"?

I am learning too, but I think that ders=class in the meaning of lesson and sınıf=class in the meaning of classroom. And you can't put sınıf or ders in the accusative here as it is the subject of the sentence. So sınıfı is definitively wrong.